LMFDB - Embedded newform 570.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 12189x^{2} - 95210x + 4841400 $ x^4 - 12189x^2 - 95210x + 4841400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$16.5544$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -230.660 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -230.660 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +628.114 q^{11} -144.000 q^{12} +803.737 q^{13} +922.640 q^{14} +225.000 q^{15} +256.000 q^{16} -802.223 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +2075.94 q^{21} -2512.46 q^{22} -2593.47 q^{23} +576.000 q^{24} +625.000 q^{25} -3214.95 q^{26} -729.000 q^{27} -3690.56 q^{28} -1932.57 q^{29} -900.000 q^{30} -4078.71 q^{31} -1024.00 q^{32} -5653.03 q^{33} +3208.89 q^{34} +5766.50 q^{35} +1296.00 q^{36} -8714.38 q^{37} -1444.00 q^{38} -7233.64 q^{39} +1600.00 q^{40} -11566.0 q^{41} -8303.76 q^{42} -8074.36 q^{43} +10049.8 q^{44} -2025.00 q^{45} +10373.9 q^{46} +3314.63 q^{47} -2304.00 q^{48} +36397.0 q^{49} -2500.00 q^{50} +7220.01 q^{51} +12859.8 q^{52} -18019.1 q^{53} +2916.00 q^{54} -15702.8 q^{55} +14762.2 q^{56} -3249.00 q^{57} +7730.29 q^{58} +13115.6 q^{59} +3600.00 q^{60} +1484.99 q^{61} +16314.8 q^{62} -18683.5 q^{63} +4096.00 q^{64} -20093.4 q^{65} +22612.1 q^{66} +67054.3 q^{67} -12835.6 q^{68} +23341.2 q^{69} -23066.0 q^{70} +2159.28 q^{71} -5184.00 q^{72} -36679.7 q^{73} +34857.5 q^{74} -5625.00 q^{75} +5776.00 q^{76} -144881. q^{77} +28934.5 q^{78} -9947.26 q^{79} -6400.00 q^{80} +6561.00 q^{81} +46263.9 q^{82} -39853.2 q^{83} +33215.0 q^{84} +20055.6 q^{85} +32297.4 q^{86} +17393.2 q^{87} -40199.3 q^{88} +131842. q^{89} +8100.00 q^{90} -185390. q^{91} -41495.5 q^{92} +36708.4 q^{93} -13258.5 q^{94} -9025.00 q^{95} +9216.00 q^{96} -107411. q^{97} -145588. q^{98} +50877.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	36.0000	0.408248
$7$	−230.660	−1.77921	−0.889605	−	0.456731i	$-0.849020\pi$
$7$	−230.660	−1.77921	−0.889605	+	0.456731i	$0.849020\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	628.114	1.56515	0.782576	−	0.622555i	$-0.213905\pi$
$11$	628.114	1.56515	0.782576	+	0.622555i	$0.213905\pi$
$12$	−144.000	−0.288675
$13$	803.737	1.31903	0.659517	−	0.751690i	$-0.270761\pi$
$13$	803.737	1.31903	0.659517	+	0.751690i	$0.270761\pi$
$14$	922.640	1.25809
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−802.223	−0.673245	−0.336622	−	0.941640i	$-0.609285\pi$
$17$	−802.223	−0.673245	−0.336622	+	0.941640i	$0.609285\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	2075.94	1.02723
$22$	−2512.46	−1.10673
$23$	−2593.47	−1.02226	−0.511130	−	0.859504i	$-0.670773\pi$
$23$	−2593.47	−1.02226	−0.511130	+	0.859504i	$0.670773\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	−3214.95	−0.932698
$27$	−729.000	−0.192450
$28$	−3690.56	−0.889605
$29$	−1932.57	−0.426718	−0.213359	−	0.976974i	$-0.568440\pi$
$29$	−1932.57	−0.426718	−0.213359	+	0.976974i	$0.568440\pi$
$30$	−900.000	−0.182574
$31$	−4078.71	−0.762287	−0.381143	−	0.924516i	$-0.624470\pi$
$31$	−4078.71	−0.762287	−0.381143	+	0.924516i	$0.624470\pi$
$32$	−1024.00	−0.176777
$33$	−5653.03	−0.903641
$34$	3208.89	0.476056
$35$	5766.50	0.795687
$36$	1296.00	0.166667
$37$	−8714.38	−1.04648	−0.523242	−	0.852184i	$-0.675277\pi$
$37$	−8714.38	−1.04648	−0.523242	+	0.852184i	$0.675277\pi$
$38$	−1444.00	−0.162221
$39$	−7233.64	−0.761544
$40$	1600.00	0.158114
$41$	−11566.0	−1.07454	−0.537270	−	0.843411i	$-0.680544\pi$
$41$	−11566.0	−1.07454	−0.537270	+	0.843411i	$0.680544\pi$
$42$	−8303.76	−0.726359
$43$	−8074.36	−0.665943	−0.332972	−	0.942937i	$-0.608051\pi$
$43$	−8074.36	−0.665943	−0.332972	+	0.942937i	$0.608051\pi$
$44$	10049.8	0.782576
$45$	−2025.00	−0.149071
$46$	10373.9	0.722846
$47$	3314.63	0.218872	0.109436	−	0.993994i	$-0.465096\pi$
$47$	3314.63	0.218872	0.109436	+	0.993994i	$0.465096\pi$
$48$	−2304.00	−0.144338
$49$	36397.0	2.16559
$50$	−2500.00	−0.141421
$51$	7220.01	0.388698
$52$	12859.8	0.659517
$53$	−18019.1	−0.881135	−0.440568	−	0.897719i	$-0.645223\pi$
$53$	−18019.1	−0.881135	−0.440568	+	0.897719i	$0.645223\pi$
$54$	2916.00	0.136083
$55$	−15702.8	−0.699958
$56$	14762.2	0.629046
$57$	−3249.00	−0.132453
$58$	7730.29	0.301735
$59$	13115.6	0.490521	0.245261	−	0.969457i	$-0.421126\pi$
$59$	13115.6	0.490521	0.245261	+	0.969457i	$0.421126\pi$
$60$	3600.00	0.129099
$61$	1484.99	0.0510973	0.0255487	−	0.999674i	$-0.491867\pi$
$61$	1484.99	0.0510973	0.0255487	+	0.999674i	$0.491867\pi$
$62$	16314.8	0.539018
$63$	−18683.5	−0.593070
$64$	4096.00	0.125000
$65$	−20093.4	−0.589890
$66$	22612.1	0.638971
$67$	67054.3	1.82490	0.912451	−	0.409186i	$-0.134187\pi$
$67$	67054.3	1.82490	0.912451	+	0.409186i	$0.134187\pi$
$68$	−12835.6	−0.336622
$69$	23341.2	0.590202
$70$	−23066.0	−0.562635
$71$	2159.28	0.0508351	0.0254176	−	0.999677i	$-0.491908\pi$
$71$	2159.28	0.0508351	0.0254176	+	0.999677i	$0.491908\pi$
$72$	−5184.00	−0.117851
$73$	−36679.7	−0.805598	−0.402799	−	0.915288i	$-0.631963\pi$
$73$	−36679.7	−0.805598	−0.402799	+	0.915288i	$0.631963\pi$
$74$	34857.5	0.739975
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−144881.	−2.78473
$78$	28934.5	0.538493
$79$	−9947.26	−0.179323	−0.0896615	−	0.995972i	$-0.528579\pi$
$79$	−9947.26	−0.179323	−0.0896615	+	0.995972i	$0.528579\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	46263.9	0.759814
$83$	−39853.2	−0.634991	−0.317496	−	0.948260i	$-0.602842\pi$
$83$	−39853.2	−0.634991	−0.317496	+	0.948260i	$0.602842\pi$
$84$	33215.0	0.513614
$85$	20055.6	0.301084
$86$	32297.4	0.470893
$87$	17393.2	0.246366
$88$	−40199.3	−0.553365
$89$	131842.	1.76433	0.882164	−	0.470942i	$-0.156086\pi$
$89$	131842.	1.76433	0.882164	+	0.470942i	$0.156086\pi$
$90$	8100.00	0.105409
$91$	−185390.	−2.34684
$92$	−41495.5	−0.511130
$93$	36708.4	0.440107
$94$	−13258.5	−0.154766
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	−107411.	−1.15910	−0.579549	−	0.814937i	$-0.696771\pi$
$97$	−107411.	−1.15910	−0.579549	+	0.814937i	$0.696771\pi$
$98$	−145588.	−1.53130
$99$	50877.2	0.521718
$100$	10000.0	0.100000
$101$	−159550.	−1.55630	−0.778149	−	0.628080i	$-0.783841\pi$
$101$	−159550.	−1.55630	−0.778149	+	0.628080i	$0.783841\pi$
$102$	−28880.0	−0.274851
$103$	−203624.	−1.89120	−0.945598	−	0.325338i	$-0.894522\pi$
$103$	−203624.	−1.89120	−0.945598	+	0.325338i	$0.894522\pi$
$104$	−51439.2	−0.466349
$105$	−51898.5	−0.459390
$106$	72076.3	0.623057
$107$	189116.	1.59687	0.798433	−	0.602084i	$-0.205663\pi$
$107$	189116.	1.59687	0.798433	+	0.602084i	$0.205663\pi$
$108$	−11664.0	−0.0962250
$109$	−99960.2	−0.805863	−0.402931	−	0.915230i	$-0.632009\pi$
$109$	−99960.2	−0.805863	−0.402931	+	0.915230i	$0.632009\pi$
$110$	62811.4	0.494945
$111$	78429.4	0.604187
$112$	−59048.9	−0.444802
$113$	169683.	1.25009	0.625045	−	0.780589i	$-0.285081\pi$
$113$	169683.	1.25009	0.625045	+	0.780589i	$0.285081\pi$
$114$	12996.0	0.0936586
$115$	64836.7	0.457168
$116$	−30921.2	−0.213359
$117$	65102.7	0.439678
$118$	−52462.4	−0.346851
$119$	185041.	1.19784
$120$	−14400.0	−0.0912871
$121$	233476.	1.44970
$122$	−5939.95	−0.0361313
$123$	104094.	0.620386
$124$	−65259.3	−0.381143
$125$	−15625.0	−0.0894427
$126$	74733.8	0.419364
$127$	105402.	0.579885	0.289942	−	0.957044i	$-0.406364\pi$
$127$	105402.	0.579885	0.289942	+	0.957044i	$0.406364\pi$
$128$	−16384.0	−0.0883883
$129$	72669.3	0.384482
$130$	80373.7	0.417115
$131$	72317.2	0.368182	0.184091	−	0.982909i	$-0.441066\pi$
$131$	72317.2	0.368182	0.184091	+	0.982909i	$0.441066\pi$
$132$	−90448.4	−0.451821
$133$	−83268.2	−0.408179
$134$	−268217.	−1.29040
$135$	18225.0	0.0860663
$136$	51342.3	0.238028
$137$	62924.0	0.286427	0.143214	−	0.989692i	$-0.454256\pi$
$137$	62924.0	0.286427	0.143214	+	0.989692i	$0.454256\pi$
$138$	−93364.8	−0.417336
$139$	62233.9	0.273206	0.136603	−	0.990626i	$-0.456382\pi$
$139$	62233.9	0.273206	0.136603	+	0.990626i	$0.456382\pi$
$140$	92264.0	0.397843
$141$	−29831.6	−0.126366
$142$	−8637.14	−0.0359459
$143$	504839.	2.06449
$144$	20736.0	0.0833333
$145$	48314.3	0.190834
$146$	146719.	0.569644
$147$	−327573.	−1.25030
$148$	−139430.	−0.523242
$149$	283411.	1.04581	0.522903	−	0.852392i	$-0.324849\pi$
$149$	283411.	1.04581	0.522903	+	0.852392i	$0.324849\pi$
$150$	22500.0	0.0816497
$151$	42673.1	0.152304	0.0761522	−	0.997096i	$-0.475737\pi$
$151$	42673.1	0.152304	0.0761522	+	0.997096i	$0.475737\pi$
$152$	−23104.0	−0.0811107
$153$	−64980.1	−0.224415
$154$	579523.	1.96910
$155$	101968.	0.340905
$156$	−115738.	−0.380772
$157$	−184848.	−0.598503	−0.299252	−	0.954174i	$-0.596737\pi$
$157$	−184848.	−0.598503	−0.299252	+	0.954174i	$0.596737\pi$
$158$	39789.0	0.126800
$159$	162172.	0.508724
$160$	25600.0	0.0790569
$161$	598209.	1.81881
$162$	−26244.0	−0.0785674
$163$	−43106.9	−0.127080	−0.0635400	−	0.997979i	$-0.520239\pi$
$163$	−43106.9	−0.127080	−0.0635400	+	0.997979i	$0.520239\pi$
$164$	−185055.	−0.537270
$165$	141326.	0.404121
$166$	159413.	0.449007
$167$	594576.	1.64974	0.824871	−	0.565321i	$-0.191248\pi$
$167$	594576.	1.64974	0.824871	+	0.565321i	$0.191248\pi$
$168$	−132860.	−0.363180
$169$	274701.	0.739849
$170$	−80222.3	−0.212899
$171$	29241.0	0.0764719
$172$	−129190.	−0.332972
$173$	437984.	1.11261	0.556305	−	0.830978i	$-0.312219\pi$
$173$	437984.	1.11261	0.556305	+	0.830978i	$0.312219\pi$
$174$	−69572.6	−0.174207
$175$	−144162.	−0.355842
$176$	160797.	0.391288
$177$	−118040.	−0.283203
$178$	−527369.	−1.24757
$179$	363304.	0.847497	0.423748	−	0.905780i	$-0.360714\pi$
$179$	363304.	0.847497	0.423748	+	0.905780i	$0.360714\pi$
$180$	−32400.0	−0.0745356
$181$	570371.	1.29408	0.647040	−	0.762456i	$-0.276007\pi$
$181$	570371.	1.29408	0.647040	+	0.762456i	$0.276007\pi$
$182$	741560.	1.65946
$183$	−13364.9	−0.0295010
$184$	165982.	0.361423
$185$	217860.	0.468001
$186$	−146834.	−0.311202
$187$	−503888.	−1.05373
$188$	53034.0	0.109436
$189$	168151.	0.342409
$190$	36100.0	0.0725476
$191$	−705980.	−1.40026	−0.700130	−	0.714015i	$-0.746875\pi$
$191$	−705980.	−1.40026	−0.700130	+	0.714015i	$0.746875\pi$
$192$	−36864.0	−0.0721688
$193$	−295276.	−0.570605	−0.285302	−	0.958438i	$-0.592094\pi$
$193$	−295276.	−0.570605	−0.285302	+	0.958438i	$0.592094\pi$
$194$	429645.	0.819606
$195$	180841.	0.340573
$196$	582352.	1.08279
$197$	−763361.	−1.40141	−0.700704	−	0.713452i	$-0.747131\pi$
$197$	−763361.	−1.40141	−0.700704	+	0.713452i	$0.747131\pi$
$198$	−203509.	−0.368910
$199$	14089.3	0.0252207	0.0126103	−	0.999920i	$-0.495986\pi$
$199$	14089.3	0.0252207	0.0126103	+	0.999920i	$0.495986\pi$
$200$	−40000.0	−0.0707107
$201$	−603489.	−1.05361
$202$	638199.	1.10047
$203$	445767.	0.759220
$204$	115520.	0.194349
$205$	289149.	0.480549
$206$	814497.	1.33728
$207$	−210071.	−0.340753
$208$	205757.	0.329758
$209$	226749.	0.359071
$210$	207594.	0.324838
$211$	402440.	0.622293	0.311147	−	0.950362i	$-0.399287\pi$
$211$	402440.	0.622293	0.311147	+	0.950362i	$0.399287\pi$
$212$	−288305.	−0.440568
$213$	−19433.6	−0.0293497
$214$	−756463.	−1.12915
$215$	201859.	0.297819
$216$	46656.0	0.0680414
$217$	940795.	1.35627
$218$	399841.	0.569831
$219$	330117.	0.465112
$220$	−251246.	−0.349979
$221$	−644777.	−0.888033
$222$	−313718.	−0.427225
$223$	443623.	0.597382	0.298691	−	0.954350i	$-0.403450\pi$
$223$	443623.	0.597382	0.298691	+	0.954350i	$0.403450\pi$
$224$	236196.	0.314523
$225$	50625.0	0.0666667
$226$	−678730.	−0.883947
$227$	231307.	0.297937	0.148968	−	0.988842i	$-0.452405\pi$
$227$	231307.	0.297937	0.148968	+	0.988842i	$0.452405\pi$
$228$	−51984.0	−0.0662266
$229$	−1.07632e6	−1.35629	−0.678146	−	0.734927i	$-0.737216\pi$
$229$	−1.07632e6	−1.35629	−0.678146	+	0.734927i	$0.737216\pi$
$230$	−259347.	−0.323267
$231$	1.30393e6	1.60777
$232$	123685.	0.150868
$233$	607415.	0.732985	0.366493	−	0.930421i	$-0.380558\pi$
$233$	607415.	0.732985	0.366493	+	0.930421i	$0.380558\pi$
$234$	−260411.	−0.310899
$235$	−82865.7	−0.0978825
$236$	209849.	0.245261
$237$	89525.4	0.103532
$238$	−740163.	−0.847003
$239$	911434.	1.03212	0.516060	−	0.856552i	$-0.327398\pi$
$239$	911434.	1.03212	0.516060	+	0.856552i	$0.327398\pi$
$240$	57600.0	0.0645497
$241$	−1.36348e6	−1.51219	−0.756097	−	0.654459i	$-0.772896\pi$
$241$	−1.36348e6	−1.51219	−0.756097	+	0.654459i	$0.772896\pi$
$242$	−933905.	−1.02509
$243$	−59049.0	−0.0641500
$244$	23759.8	0.0255487
$245$	−909925.	−0.968480
$246$	−416375.	−0.438679
$247$	290149.	0.302607
$248$	261037.	0.269509
$249$	358679.	0.366612
$250$	62500.0	0.0632456
$251$	121108.	0.121336	0.0606680	−	0.998158i	$-0.480677\pi$
$251$	121108.	0.121336	0.0606680	+	0.998158i	$0.480677\pi$
$252$	−298935.	−0.296535
$253$	−1.62899e6	−1.59999
$254$	−421610.	−0.410040
$255$	−180500.	−0.173831
$256$	65536.0	0.0625000
$257$	102803.	0.0970899	0.0485450	−	0.998821i	$-0.484542\pi$
$257$	102803.	0.0970899	0.0485450	+	0.998821i	$0.484542\pi$
$258$	−290677.	−0.271870
$259$	2.01006e6	1.86191
$260$	−321495.	−0.294945
$261$	−156538.	−0.142239
$262$	−289269.	−0.260344
$263$	1.81366e6	1.61684	0.808418	−	0.588609i	$-0.200324\pi$
$263$	1.81366e6	1.61684	0.808418	+	0.588609i	$0.200324\pi$
$264$	361794.	0.319485
$265$	450477.	0.394056
$266$	333073.	0.288626
$267$	−1.18658e6	−1.01864
$268$	1.07287e6	0.912451
$269$	−1.01936e6	−0.858907	−0.429454	−	0.903089i	$-0.641294\pi$
$269$	−1.01936e6	−0.858907	−0.429454	+	0.903089i	$0.641294\pi$
$270$	−72900.0	−0.0608581
$271$	1.86672e6	1.54403	0.772017	−	0.635602i	$-0.219248\pi$
$271$	1.86672e6	1.54403	0.772017	+	0.635602i	$0.219248\pi$
$272$	−205369.	−0.168311
$273$	1.66851e6	1.35495
$274$	−251696.	−0.202535
$275$	392571.	0.313031
$276$	373459.	0.295101
$277$	682005.	0.534057	0.267029	−	0.963689i	$-0.413958\pi$
$277$	682005.	0.534057	0.267029	+	0.963689i	$0.413958\pi$
$278$	−248936.	−0.193186
$279$	−330375.	−0.254096
$280$	−369056.	−0.281318
$281$	−488572.	−0.369116	−0.184558	−	0.982822i	$-0.559085\pi$
$281$	−488572.	−0.369116	−0.184558	+	0.982822i	$0.559085\pi$
$282$	119327.	0.0893541
$283$	−1.37179e6	−1.01818	−0.509088	−	0.860715i	$-0.670017\pi$
$283$	−1.37179e6	−1.01818	−0.509088	+	0.860715i	$0.670017\pi$
$284$	34548.6	0.0254176
$285$	81225.0	0.0592349
$286$	−2.01935e6	−1.45981
$287$	2.66781e6	1.91183
$288$	−82944.0	−0.0589256
$289$	−776294.	−0.546741
$290$	−193257.	−0.134940
$291$	966701.	0.669206
$292$	−586875.	−0.402799
$293$	2.10709e6	1.43388	0.716942	−	0.697133i	$-0.245541\pi$
$293$	2.10709e6	1.43388	0.716942	+	0.697133i	$0.245541\pi$
$294$	1.31029e6	0.884097
$295$	−327890.	−0.219368
$296$	557720.	0.369988
$297$	−457895.	−0.301214
$298$	−1.13364e6	−0.739497
$299$	−2.08447e6	−1.34839
$300$	−90000.0	−0.0577350
$301$	1.86243e6	1.18485
$302$	−170693.	−0.107695
$303$	1.43595e6	0.898529
$304$	92416.0	0.0573539
$305$	−37124.7	−0.0228514
$306$	259920.	0.158685
$307$	−1.33960e6	−0.811204	−0.405602	−	0.914050i	$-0.632938\pi$
$307$	−1.33960e6	−0.811204	−0.405602	+	0.914050i	$0.632938\pi$
$308$	−2.31809e6	−1.39237
$309$	1.83262e6	1.09188
$310$	−407871.	−0.241056
$311$	1.25074e6	0.733272	0.366636	−	0.930364i	$-0.380509\pi$
$311$	1.25074e6	0.733272	0.366636	+	0.930364i	$0.380509\pi$
$312$	462953.	0.269247
$313$	3.12896e6	1.80526	0.902629	−	0.430420i	$-0.141634\pi$
$313$	3.12896e6	1.80526	0.902629	+	0.430420i	$0.141634\pi$
$314$	739393.	0.423206
$315$	467086.	0.265229
$316$	−159156.	−0.0896615
$317$	−1.89301e6	−1.05805	−0.529023	−	0.848607i	$-0.677442\pi$
$317$	−1.89301e6	−1.05805	−0.529023	+	0.848607i	$0.677442\pi$
$318$	−648686.	−0.359722
$319$	−1.21388e6	−0.667879
$320$	−102400.	−0.0559017
$321$	−1.70204e6	−0.921951
$322$	−2.39284e6	−1.28610
$323$	−289603.	−0.154453
$324$	104976.	0.0555556
$325$	502336.	0.263807
$326$	172427.	0.0898592
$327$	899642.	0.465265
$328$	740222.	0.379907
$329$	−764552.	−0.389419
$330$	−565303.	−0.285756
$331$	−1.25423e6	−0.629228	−0.314614	−	0.949220i	$-0.601875\pi$
$331$	−1.25423e6	−0.629228	−0.314614	+	0.949220i	$0.601875\pi$
$332$	−637651.	−0.317496
$333$	−705865.	−0.348828
$334$	−2.37830e6	−1.16654
$335$	−1.67636e6	−0.816121
$336$	531441.	0.256807
$337$	2.73072e6	1.30979	0.654895	−	0.755719i	$-0.272713\pi$
$337$	2.73072e6	1.30979	0.654895	+	0.755719i	$0.272713\pi$
$338$	−1.09880e6	−0.523152
$339$	−1.52714e6	−0.721739
$340$	320889.	0.150542
$341$	−2.56189e6	−1.19310
$342$	−116964.	−0.0540738
$343$	−4.51863e6	−2.07382
$344$	516759.	0.235446
$345$	−583530.	−0.263946
$346$	−1.75194e6	−0.786734
$347$	2.16827e6	0.966694	0.483347	−	0.875429i	$-0.339421\pi$
$347$	2.16827e6	0.966694	0.483347	+	0.875429i	$0.339421\pi$
$348$	278290.	0.123183
$349$	1.76599e6	0.776111	0.388055	−	0.921636i	$-0.373147\pi$
$349$	1.76599e6	0.776111	0.388055	+	0.921636i	$0.373147\pi$
$350$	576650.	0.251618
$351$	−585925.	−0.253848
$352$	−643189.	−0.276683
$353$	−2.55077e6	−1.08952	−0.544759	−	0.838592i	$-0.683379\pi$
$353$	−2.55077e6	−1.08952	−0.544759	+	0.838592i	$0.683379\pi$
$354$	472161.	0.200254
$355$	−53982.1	−0.0227342
$356$	2.10948e6	0.882164
$357$	−1.66537e6	−0.691575
$358$	−1.45322e6	−0.599271
$359$	228818.	0.0937030	0.0468515	−	0.998902i	$-0.485081\pi$
$359$	228818.	0.0937030	0.0468515	+	0.998902i	$0.485081\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−2.28148e6	−0.915053
$363$	−2.10129e6	−0.836986
$364$	−2.96624e6	−1.17342
$365$	916992.	0.360274
$366$	53459.5	0.0208604
$367$	3.55074e6	1.37611	0.688056	−	0.725657i	$-0.258464\pi$
$367$	3.55074e6	1.37611	0.688056	+	0.725657i	$0.258464\pi$
$368$	−663927.	−0.255565
$369$	−936843.	−0.358180
$370$	−871438.	−0.330927
$371$	4.15628e6	1.56772
$372$	587334.	0.220053
$373$	−3.75192e6	−1.39631	−0.698155	−	0.715947i	$-0.745995\pi$
$373$	−3.75192e6	−1.39631	−0.698155	+	0.715947i	$0.745995\pi$
$374$	2.01555e6	0.745100
$375$	140625.	0.0516398
$376$	−212136.	−0.0773829
$377$	−1.55328e6	−0.562855
$378$	−672604.	−0.242120
$379$	−5.35763e6	−1.91591	−0.957954	−	0.286922i	$-0.907368\pi$
$379$	−5.35763e6	−1.91591	−0.957954	+	0.286922i	$0.907368\pi$
$380$	−144400.	−0.0512989
$381$	−948622.	−0.334796
$382$	2.82392e6	0.990134
$383$	191544.	0.0667223	0.0333612	−	0.999443i	$-0.489379\pi$
$383$	191544.	0.0667223	0.0333612	+	0.999443i	$0.489379\pi$
$384$	147456.	0.0510310
$385$	3.62202e6	1.24537
$386$	1.18111e6	0.403479
$387$	−654023.	−0.221981
$388$	−1.71858e6	−0.579549
$389$	700278.	0.234637	0.117318	−	0.993094i	$-0.462570\pi$
$389$	700278.	0.234637	0.117318	+	0.993094i	$0.462570\pi$
$390$	−723364.	−0.240821
$391$	2.08054e6	0.688231
$392$	−2.32941e6	−0.765650
$393$	−650854.	−0.212570
$394$	3.05344e6	0.990945
$395$	248682.	0.0801957
$396$	814036.	0.260859
$397$	−394762.	−0.125707	−0.0628534	−	0.998023i	$-0.520020\pi$
$397$	−394762.	−0.125707	−0.0628534	+	0.998023i	$0.520020\pi$
$398$	−56357.2	−0.0178337
$399$	749414.	0.235662
$400$	160000.	0.0500000
$401$	2.56287e6	0.795913	0.397957	−	0.917404i	$-0.369719\pi$
$401$	2.56287e6	0.795913	0.397957	+	0.917404i	$0.369719\pi$
$402$	2.41395e6	0.745013
$403$	−3.27821e6	−1.00548
$404$	−2.55280e6	−0.778149
$405$	−164025.	−0.0496904
$406$	−1.78307e6	−0.536850
$407$	−5.47362e6	−1.63791
$408$	−462081.	−0.137426
$409$	6.46480e6	1.91094	0.955469	−	0.295091i	$-0.0953499\pi$
$409$	6.46480e6	1.91094	0.955469	+	0.295091i	$0.0953499\pi$
$410$	−1.15660e6	−0.339799
$411$	−566316.	−0.165369
$412$	−3.25799e6	−0.945598
$413$	−3.02524e6	−0.872740
$414$	840283.	0.240949
$415$	996329.	0.283977
$416$	−823027.	−0.233174
$417$	−560105.	−0.157735
$418$	−906997.	−0.253901
$419$	5.82957e6	1.62219	0.811094	−	0.584916i	$-0.198872\pi$
$419$	5.82957e6	1.62219	0.811094	+	0.584916i	$0.198872\pi$
$420$	−830376.	−0.229695
$421$	2.47417e6	0.680337	0.340168	−	0.940365i	$-0.389516\pi$
$421$	2.47417e6	0.680337	0.340168	+	0.940365i	$0.389516\pi$
$422$	−1.60976e6	−0.440028
$423$	268485.	0.0729573
$424$	1.15322e6	0.311528
$425$	−501390.	−0.134649
$426$	77734.3	0.0207534
$427$	−342527.	−0.0909128
$428$	3.02585e6	0.798433
$429$	−4.54355e6	−1.19193
$430$	−807436.	−0.210590
$431$	4.69704e6	1.21796	0.608978	−	0.793187i	$-0.291580\pi$
$431$	4.69704e6	1.21796	0.608978	+	0.793187i	$0.291580\pi$
$432$	−186624.	−0.0481125
$433$	4.26680e6	1.09366	0.546831	−	0.837243i	$-0.315834\pi$
$433$	4.26680e6	1.09366	0.546831	+	0.837243i	$0.315834\pi$
$434$	−3.76318e6	−0.959026
$435$	−434829.	−0.110178
$436$	−1.59936e6	−0.402931
$437$	−936241.	−0.234522
$438$	−1.32047e6	−0.328884
$439$	−4.92906e6	−1.22068	−0.610341	−	0.792138i	$-0.708968\pi$
$439$	−4.92906e6	−1.22068	−0.610341	+	0.792138i	$0.708968\pi$
$440$	1.00498e6	0.247472
$441$	2.94816e6	0.721862
$442$	2.57911e6	0.627934
$443$	1.92446e6	0.465907	0.232953	−	0.972488i	$-0.425161\pi$
$443$	1.92446e6	0.465907	0.232953	+	0.972488i	$0.425161\pi$
$444$	1.25487e6	0.302094
$445$	−3.29606e6	−0.789032
$446$	−1.77449e6	−0.422413
$447$	−2.55070e6	−0.603797
$448$	−944783.	−0.222401
$449$	2.96087e6	0.693112	0.346556	−	0.938029i	$-0.387351\pi$
$449$	2.96087e6	0.693112	0.346556	+	0.938029i	$0.387351\pi$
$450$	−202500.	−0.0471405
$451$	−7.26475e6	−1.68182
$452$	2.71492e6	0.625045
$453$	−384058.	−0.0879329
$454$	−925228.	−0.210673
$455$	4.63475e6	1.04954
$456$	207936.	0.0468293
$457$	6.45680e6	1.44620	0.723098	−	0.690746i	$-0.242718\pi$
$457$	6.45680e6	1.44620	0.723098	+	0.690746i	$0.242718\pi$
$458$	4.30529e6	0.959044
$459$	584821.	0.129566
$460$	1.03739e6	0.228584
$461$	6.69970e6	1.46826	0.734130	−	0.679009i	$-0.237590\pi$
$461$	6.69970e6	1.46826	0.734130	+	0.679009i	$0.237590\pi$
$462$	−5.21571e6	−1.13686
$463$	−7.78592e6	−1.68794	−0.843971	−	0.536389i	$-0.819788\pi$
$463$	−7.78592e6	−1.68794	−0.843971	+	0.536389i	$0.819788\pi$
$464$	−494739.	−0.106679
$465$	−917709.	−0.196822
$466$	−2.42966e6	−0.518299
$467$	18189.6	0.00385950	0.00192975	−	0.999998i	$-0.499386\pi$
$467$	18189.6	0.00385950	0.00192975	+	0.999998i	$0.499386\pi$
$468$	1.04164e6	0.219839
$469$	−1.54667e7	−3.24688
$470$	331463.	0.0692134
$471$	1.66363e6	0.345546
$472$	−839398.	−0.173425
$473$	−5.07162e6	−1.04230
$474$	−358101.	−0.0732083
$475$	225625.	0.0458831
$476$	2.96065e6	0.598922
$477$	−1.45954e6	−0.293712
$478$	−3.64574e6	−0.729819
$479$	6.97302e6	1.38862	0.694308	−	0.719678i	$-0.255711\pi$
$479$	6.97302e6	1.38862	0.694308	+	0.719678i	$0.255711\pi$
$480$	−230400.	−0.0456435
$481$	−7.00407e6	−1.38035
$482$	5.45394e6	1.06928
$483$	−5.38388e6	−1.05009
$484$	3.73562e6	0.724852
$485$	2.68528e6	0.518364
$486$	236196.	0.0453609
$487$	−5.52885e6	−1.05636	−0.528181	−	0.849132i	$-0.677126\pi$
$487$	−5.52885e6	−1.05636	−0.528181	+	0.849132i	$0.677126\pi$
$488$	−95039.2	−0.0180656
$489$	387962.	0.0733697
$490$	3.63970e6	0.684819
$491$	−8.15752e6	−1.52705	−0.763527	−	0.645776i	$-0.776534\pi$
$491$	−8.15752e6	−1.52705	−0.763527	+	0.645776i	$0.776534\pi$
$492$	1.66550e6	0.310193
$493$	1.55035e6	0.287286
$494$	−1.16060e6	−0.213975
$495$	−1.27193e6	−0.233319
$496$	−1.04415e6	−0.190572
$497$	−498061.	−0.0904464
$498$	−1.43471e6	−0.259234
$499$	8.91750e6	1.60321	0.801607	−	0.597851i	$-0.203978\pi$
$499$	8.91750e6	1.60321	0.801607	+	0.597851i	$0.203978\pi$
$500$	−250000.	−0.0447214
$501$	−5.35118e6	−0.952479
$502$	−484433.	−0.0857974
$503$	4.45740e6	0.785527	0.392764	−	0.919639i	$-0.371519\pi$
$503$	4.45740e6	0.785527	0.392764	+	0.919639i	$0.371519\pi$
$504$	1.19574e6	0.209682
$505$	3.98874e6	0.695998
$506$	6.51597e6	1.13137
$507$	−2.47231e6	−0.427152
$508$	1.68644e6	0.289942
$509$	4.54355e6	0.777322	0.388661	−	0.921381i	$-0.372938\pi$
$509$	4.54355e6	0.777322	0.388661	+	0.921381i	$0.372938\pi$
$510$	722001.	0.122917
$511$	8.46053e6	1.43333
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−411213.	−0.0686530
$515$	5.09061e6	0.845768
$516$	1.16271e6	0.192241
$517$	2.08196e6	0.342568
$518$	−8.04023e6	−1.31657
$519$	−3.94186e6	−0.642366
$520$	1.28598e6	0.208558
$521$	−1.00127e7	−1.61606	−0.808028	−	0.589145i	$-0.799465\pi$
$521$	−1.00127e7	−1.61606	−0.808028	+	0.589145i	$0.799465\pi$
$522$	626153.	0.100578
$523$	−2.38406e6	−0.381122	−0.190561	−	0.981675i	$-0.561031\pi$
$523$	−2.38406e6	−0.381122	−0.190561	+	0.981675i	$0.561031\pi$
$524$	1.15707e6	0.184091
$525$	1.29746e6	0.205445
$526$	−7.25463e6	−1.14328
$527$	3.27204e6	0.513206
$528$	−1.44717e6	−0.225910
$529$	289726.	0.0450141
$530$	−1.80191e6	−0.278639
$531$	1.06236e6	0.163507
$532$	−1.33229e6	−0.204089
$533$	−9.29600e6	−1.41735
$534$	4.74632e6	0.720284
$535$	−4.72790e6	−0.714140
$536$	−4.29147e6	−0.645200
$537$	−3.26974e6	−0.489302
$538$	4.07743e6	0.607339
$539$	2.28615e7	3.38947
$540$	291600.	0.0430331
$541$	−8.90731e6	−1.30844	−0.654220	−	0.756305i	$-0.727003\pi$
$541$	−8.90731e6	−1.30844	−0.654220	+	0.756305i	$0.727003\pi$
$542$	−7.46689e6	−1.09180
$543$	−5.13334e6	−0.747137
$544$	821477.	0.119014
$545$	2.49901e6	0.360393
$546$	−6.67404e6	−0.958092
$547$	7.97575e6	1.13973	0.569867	−	0.821737i	$-0.306995\pi$
$547$	7.97575e6	1.13973	0.569867	+	0.821737i	$0.306995\pi$
$548$	1.00678e6	0.143214
$549$	120284.	0.0170324
$550$	−1.57028e6	−0.221346
$551$	−697659.	−0.0978958
$552$	−1.49384e6	−0.208668
$553$	2.29443e6	0.319053
$554$	−2.72802e6	−0.377636
$555$	−1.96074e6	−0.270201
$556$	995742.	0.136603
$557$	6.13369e6	0.837691	0.418845	−	0.908058i	$-0.362435\pi$
$557$	6.13369e6	0.837691	0.418845	+	0.908058i	$0.362435\pi$
$558$	1.32150e6	0.179673
$559$	−6.48967e6	−0.878401
$560$	1.47622e6	0.198922
$561$	4.53499e6	0.608372
$562$	1.95429e6	0.261004
$563$	−1.38756e7	−1.84493	−0.922466	−	0.386079i	$-0.873829\pi$
$563$	−1.38756e7	−1.84493	−0.922466	+	0.386079i	$0.873829\pi$
$564$	−477306.	−0.0631829
$565$	−4.24206e6	−0.559057
$566$	5.48717e6	0.719959
$567$	−1.51336e6	−0.197690
$568$	−138194.	−0.0179729
$569$	−3.69821e6	−0.478863	−0.239431	−	0.970913i	$-0.576961\pi$
$569$	−3.69821e6	−0.478863	−0.239431	+	0.970913i	$0.576961\pi$
$570$	−324900.	−0.0418854
$571$	−6.18422e6	−0.793770	−0.396885	−	0.917868i	$-0.629909\pi$
$571$	−6.18422e6	−0.793770	−0.396885	+	0.917868i	$0.629909\pi$
$572$	8.07742e6	1.03224
$573$	6.35382e6	0.808441
$574$	−1.06712e7	−1.35187
$575$	−1.62092e6	−0.204452
$576$	331776.	0.0416667
$577$	−5.84711e6	−0.731142	−0.365571	−	0.930784i	$-0.619126\pi$
$577$	−5.84711e6	−0.731142	−0.365571	+	0.930784i	$0.619126\pi$
$578$	3.10518e6	0.386604
$579$	2.65749e6	0.329439
$580$	773029.	0.0954170
$581$	9.19253e6	1.12978
$582$	−3.86680e6	−0.473200
$583$	−1.13180e7	−1.37911
$584$	2.34750e6	0.284822
$585$	−1.62757e6	−0.196630
$586$	−8.42836e6	−1.01391
$587$	1.02652e6	0.122962	0.0614812	−	0.998108i	$-0.480418\pi$
$587$	1.02652e6	0.122962	0.0614812	+	0.998108i	$0.480418\pi$
$588$	−5.24117e6	−0.625151
$589$	−1.47241e6	−0.174881
$590$	1.31156e6	0.155116
$591$	6.87025e6	0.809103
$592$	−2.23088e6	−0.261621
$593$	−2.70408e6	−0.315778	−0.157889	−	0.987457i	$-0.550469\pi$
$593$	−2.70408e6	−0.315778	−0.157889	+	0.987457i	$0.550469\pi$
$594$	1.83158e6	0.212990
$595$	−4.62602e6	−0.535692
$596$	4.53458e6	0.522903
$597$	−126804.	−0.0145612
$598$	8.33786e6	0.953459
$599$	8.16463e6	0.929757	0.464879	−	0.885374i	$-0.346098\pi$
$599$	8.16463e6	0.929757	0.464879	+	0.885374i	$0.346098\pi$
$600$	360000.	0.0408248
$601$	1.27869e7	1.44404	0.722021	−	0.691872i	$-0.243214\pi$
$601$	1.27869e7	1.44404	0.722021	+	0.691872i	$0.243214\pi$
$602$	−7.44973e6	−0.837817
$603$	5.43140e6	0.608301
$604$	682770.	0.0761522
$605$	−5.83690e6	−0.648327
$606$	−5.74379e6	−0.635356
$607$	5.96086e6	0.656654	0.328327	−	0.944564i	$-0.393515\pi$
$607$	5.96086e6	0.656654	0.328327	+	0.944564i	$0.393515\pi$
$608$	−369664.	−0.0405554
$609$	−4.01190e6	−0.438336
$610$	148499.	0.0161584
$611$	2.66409e6	0.288699
$612$	−1.03968e6	−0.112207
$613$	3.45603e6	0.371472	0.185736	−	0.982600i	$-0.440533\pi$
$613$	3.45603e6	0.371472	0.185736	+	0.982600i	$0.440533\pi$
$614$	5.35841e6	0.573608
$615$	−2.60234e6	−0.277445
$616$	9.27237e6	0.984552
$617$	7.84481e6	0.829601	0.414801	−	0.909912i	$-0.363851\pi$
$617$	7.84481e6	0.829601	0.414801	+	0.909912i	$0.363851\pi$
$618$	−7.33047e6	−0.772077
$619$	1.06480e7	1.11697	0.558484	−	0.829515i	$-0.311383\pi$
$619$	1.06480e7	1.11697	0.558484	+	0.829515i	$0.311383\pi$
$620$	1.63148e6	0.170453
$621$	1.89064e6	0.196734
$622$	−5.00295e6	−0.518502
$623$	−3.04107e7	−3.13911
$624$	−1.85181e6	−0.190386
$625$	390625.	0.0400000
$626$	−1.25158e7	−1.27651
$627$	−2.04074e6	−0.207310
$628$	−2.95757e6	−0.299252
$629$	6.99088e6	0.704539
$630$	−1.86835e6	−0.187545
$631$	1.48911e7	1.48886	0.744428	−	0.667703i	$-0.232722\pi$
$631$	1.48911e7	1.48886	0.744428	+	0.667703i	$0.232722\pi$
$632$	636625.	0.0634002
$633$	−3.62196e6	−0.359281
$634$	7.57204e6	0.748152
$635$	−2.63506e6	−0.259332
$636$	2.59475e6	0.254362
$637$	2.92536e7	2.85648
$638$	4.85550e6	0.472261
$639$	174902.	0.0169450
$640$	409600.	0.0395285
$641$	8.03932e6	0.772813	0.386406	−	0.922329i	$-0.373716\pi$
$641$	8.03932e6	0.772813	0.386406	+	0.922329i	$0.373716\pi$
$642$	6.80817e6	0.651918
$643$	−1.14914e7	−1.09608	−0.548042	−	0.836451i	$-0.684627\pi$
$643$	−1.14914e7	−1.09608	−0.548042	+	0.836451i	$0.684627\pi$
$644$	9.57134e6	0.909407
$645$	−1.81673e6	−0.171946
$646$	1.15841e6	0.109215
$647$	1.38093e7	1.29692	0.648458	−	0.761250i	$-0.275414\pi$
$647$	1.38093e7	1.29692	0.648458	+	0.761250i	$0.275414\pi$
$648$	−419904.	−0.0392837
$649$	8.23809e6	0.767741
$650$	−2.00934e6	−0.186540
$651$	−8.46715e6	−0.783042
$652$	−689710.	−0.0635400
$653$	−3.02262e6	−0.277396	−0.138698	−	0.990335i	$-0.544292\pi$
$653$	−3.02262e6	−0.277396	−0.138698	+	0.990335i	$0.544292\pi$
$654$	−3.59857e6	−0.328992
$655$	−1.80793e6	−0.164656
$656$	−2.96089e6	−0.268635
$657$	−2.97105e6	−0.268533
$658$	3.05821e6	0.275361
$659$	2.10918e7	1.89191	0.945955	−	0.324298i	$-0.105128\pi$
$659$	2.10918e7	1.89191	0.945955	+	0.324298i	$0.105128\pi$
$660$	2.26121e6	0.202060
$661$	−1.71105e7	−1.52320	−0.761602	−	0.648045i	$-0.775587\pi$
$661$	−1.71105e7	−1.52320	−0.761602	+	0.648045i	$0.775587\pi$
$662$	5.01693e6	0.444932
$663$	5.80299e6	0.512706
$664$	2.55060e6	0.224503
$665$	2.08171e6	0.182543
$666$	2.82346e6	0.246658
$667$	5.01206e6	0.436216
$668$	9.51321e6	0.824871
$669$	−3.99261e6	−0.344899
$670$	6.70543e6	0.577085
$671$	932741.	0.0799751
$672$	−2.12576e6	−0.181590
$673$	−1.38710e7	−1.18051	−0.590254	−	0.807218i	$-0.700972\pi$
$673$	−1.38710e7	−1.18051	−0.590254	+	0.807218i	$0.700972\pi$
$674$	−1.09229e7	−0.926162
$675$	−455625.	−0.0384900
$676$	4.39521e6	0.369925
$677$	−6.91509e6	−0.579864	−0.289932	−	0.957047i	$-0.593633\pi$
$677$	−6.91509e6	−0.579864	−0.289932	+	0.957047i	$0.593633\pi$
$678$	6.10857e6	0.510347
$679$	2.47755e7	2.06228
$680$	−1.28356e6	−0.106449
$681$	−2.08176e6	−0.172014
$682$	1.02476e7	0.843646
$683$	10968.6	0.000899705 0	0.000449852	−	1.00000i	$-0.499857\pi$
$683$	10968.6	0.000899705 0	0.000449852		1.00000i	$0.499857\pi$
$684$	467856.	0.0382360
$685$	−1.57310e6	−0.128094
$686$	1.80745e7	1.46641
$687$	9.68690e6	0.783056
$688$	−2.06704e6	−0.166486
$689$	−1.44826e7	−1.16225
$690$	2.33412e6	0.186638
$691$	2.35611e6	0.187715	0.0938577	−	0.995586i	$-0.470080\pi$
$691$	2.35611e6	0.187715	0.0938577	+	0.995586i	$0.470080\pi$
$692$	7.00774e6	0.556305
$693$	−1.17353e7	−0.928245
$694$	−8.67307e6	−0.683556
$695$	−1.55585e6	−0.122181
$696$	−1.11316e6	−0.0871034
$697$	9.27849e6	0.723428
$698$	−7.06394e6	−0.548793
$699$	−5.46673e6	−0.423189
$700$	−2.30660e6	−0.177921
$701$	−1.85411e7	−1.42508	−0.712540	−	0.701631i	$-0.752455\pi$
$701$	−1.85411e7	−1.42508	−0.712540	+	0.701631i	$0.752455\pi$
$702$	2.34370e6	0.179498
$703$	−3.14589e6	−0.240080
$704$	2.57275e6	0.195644
$705$	745791.	0.0565125
$706$	1.02031e7	0.770406
$707$	3.68017e7	2.76898
$708$	−1.88865e6	−0.141601
$709$	−2.90397e6	−0.216959	−0.108479	−	0.994099i	$-0.534598\pi$
$709$	−2.90397e6	−0.216959	−0.108479	+	0.994099i	$0.534598\pi$
$710$	215928.	0.0160755
$711$	−805728.	−0.0597743
$712$	−8.43790e6	−0.623784
$713$	1.05780e7	0.779255
$714$	6.66147e6	0.489018
$715$	−1.26210e7	−0.923267
$716$	5.81287e6	0.423748
$717$	−8.20290e6	−0.595895
$718$	−915271.	−0.0662580
$719$	−9.34339e6	−0.674035	−0.337017	−	0.941498i	$-0.609418\pi$
$719$	−9.34339e6	−0.674035	−0.337017	+	0.941498i	$0.609418\pi$
$720$	−518400.	−0.0372678
$721$	4.69680e7	3.36483
$722$	−521284.	−0.0372161
$723$	1.22714e7	0.873066
$724$	9.12594e6	0.647040
$725$	−1.20786e6	−0.0853436
$726$	8.40514e6	0.591839
$727$	1.36926e7	0.960835	0.480417	−	0.877040i	$-0.340485\pi$
$727$	1.36926e7	0.960835	0.480417	+	0.877040i	$0.340485\pi$
$728$	1.18650e7	0.829732
$729$	531441.	0.0370370
$730$	−3.66797e6	−0.254752
$731$	6.47744e6	0.448343
$732$	−213838.	−0.0147505
$733$	1.10514e7	0.759725	0.379862	−	0.925043i	$-0.375971\pi$
$733$	1.10514e7	0.759725	0.379862	+	0.925043i	$0.375971\pi$
$734$	−1.42030e7	−0.973058
$735$	8.18933e6	0.559152
$736$	2.65571e6	0.180712
$737$	4.21177e7	2.85625
$738$	3.74737e6	0.253271
$739$	1.74381e7	1.17460	0.587299	−	0.809370i	$-0.300191\pi$
$739$	1.74381e7	1.17460	0.587299	+	0.809370i	$0.300191\pi$
$740$	3.48575e6	0.234001
$741$	−2.61134e6	−0.174710
$742$	−1.66251e7	−1.10855
$743$	−1.62135e7	−1.07747	−0.538733	−	0.842477i	$-0.681097\pi$
$743$	−1.62135e7	−1.07747	−0.538733	+	0.842477i	$0.681097\pi$
$744$	−2.34934e6	−0.155601
$745$	−7.08528e6	−0.467699
$746$	1.50077e7	0.987340
$747$	−3.22811e6	−0.211664
$748$	−8.06220e6	−0.526866
$749$	−4.36215e7	−2.84116
$750$	−562500.	−0.0365148
$751$	−5.97551e6	−0.386612	−0.193306	−	0.981139i	$-0.561921\pi$
$751$	−5.97551e6	−0.386612	−0.193306	+	0.981139i	$0.561921\pi$
$752$	848544.	0.0547180
$753$	−1.08997e6	−0.0700533
$754$	6.21312e6	0.397999
$755$	−1.06683e6	−0.0681126
$756$	2.69042e6	0.171205
$757$	1.89382e7	1.20116	0.600579	−	0.799565i	$-0.294937\pi$
$757$	1.89382e7	1.20116	0.600579	+	0.799565i	$0.294937\pi$
$758$	2.14305e7	1.35475
$759$	1.46609e7	0.923756
$760$	577600.	0.0362738
$761$	2.64663e7	1.65666	0.828328	−	0.560244i	$-0.189293\pi$
$761$	2.64663e7	1.65666	0.828328	+	0.560244i	$0.189293\pi$
$762$	3.79449e6	0.236737
$763$	2.30568e7	1.43380
$764$	−1.12957e7	−0.700130
$765$	1.62450e6	0.100361
$766$	−766175.	−0.0471798
$767$	1.05415e7	0.647014
$768$	−589824.	−0.0360844
$769$	−2.40056e7	−1.46385	−0.731926	−	0.681384i	$-0.761378\pi$
$769$	−2.40056e7	−1.46385	−0.731926	+	0.681384i	$0.761378\pi$
$770$	−1.44881e7	−0.880610
$771$	−925230.	−0.0560549
$772$	−4.72442e6	−0.285302
$773$	−2.08597e7	−1.25562	−0.627811	−	0.778366i	$-0.716049\pi$
$773$	−2.08597e7	−1.25562	−0.627811	+	0.778366i	$0.716049\pi$
$774$	2.61609e6	0.156964
$775$	−2.54919e6	−0.152457
$776$	6.87432e6	0.409803
$777$	−1.80905e7	−1.07498
$778$	−2.80111e6	−0.165913
$779$	−4.17531e6	−0.246516
$780$	2.89345e6	0.170286
$781$	1.35628e6	0.0795648
$782$	−8.32216e6	−0.486653
$783$	1.40885e6	0.0821219
$784$	9.31764e6	0.541397
$785$	4.62121e6	0.267659
$786$	2.60342e6	0.150310
$787$	−5.79192e6	−0.333338	−0.166669	−	0.986013i	$-0.553301\pi$
$787$	−5.79192e6	−0.333338	−0.166669	+	0.986013i	$0.553301\pi$
$788$	−1.22138e7	−0.700704
$789$	−1.63229e7	−0.933481
$790$	−994726.	−0.0567069
$791$	−3.91390e7	−2.22417
$792$	−3.25614e6	−0.184455
$793$	1.19354e6	0.0673991
$794$	1.57905e6	0.0888882
$795$	−4.05429e6	−0.227508
$796$	225429.	0.0126103
$797$	−5.43418e6	−0.303032	−0.151516	−	0.988455i	$-0.548415\pi$
$797$	−5.43418e6	−0.303032	−0.151516	+	0.988455i	$0.548415\pi$
$798$	−2.99766e6	−0.166638
$799$	−2.65907e6	−0.147354
$800$	−640000.	−0.0353553
$801$	1.06792e7	0.588110
$802$	−1.02515e7	−0.562796
$803$	−2.30390e7	−1.26088
$804$	−9.65582e6	−0.526804
$805$	−1.49552e7	−0.813398
$806$	1.31128e7	0.710983
$807$	9.17423e6	0.495890
$808$	1.02112e7	0.550234
$809$	−3.31836e6	−0.178259	−0.0891295	−	0.996020i	$-0.528409\pi$
$809$	−3.31836e6	−0.178259	−0.0891295	+	0.996020i	$0.528409\pi$
$810$	656100.	0.0351364
$811$	−1.16281e7	−0.620805	−0.310403	−	0.950605i	$-0.600464\pi$
$811$	−1.16281e7	−0.620805	−0.310403	+	0.950605i	$0.600464\pi$
$812$	7.13227e6	0.379610
$813$	−1.68005e7	−0.891448
$814$	2.18945e7	1.15817
$815$	1.07767e6	0.0568319
$816$	1.84832e6	0.0971745
$817$	−2.91484e6	−0.152778
$818$	−2.58592e7	−1.35124
$819$	−1.50166e7	−0.782279
$820$	4.62639e6	0.240274
$821$	−2.48220e7	−1.28523	−0.642613	−	0.766191i	$-0.722150\pi$
$821$	−2.48220e7	−1.28523	−0.642613	+	0.766191i	$0.722150\pi$
$822$	2.26526e6	0.116934
$823$	1.30084e7	0.669457	0.334729	−	0.942315i	$-0.391355\pi$
$823$	1.30084e7	0.669457	0.334729	+	0.942315i	$0.391355\pi$
$824$	1.30320e7	0.668639
$825$	−3.53314e6	−0.180728
$826$	1.21010e7	0.617121
$827$	−2.61265e6	−0.132837	−0.0664183	−	0.997792i	$-0.521157\pi$
$827$	−2.61265e6	−0.132837	−0.0664183	+	0.997792i	$0.521157\pi$
$828$	−3.36113e6	−0.170377
$829$	−2.42946e7	−1.22779	−0.613895	−	0.789388i	$-0.710398\pi$
$829$	−2.42946e7	−1.22779	−0.613895	+	0.789388i	$0.710398\pi$
$830$	−3.98532e6	−0.200802
$831$	−6.13804e6	−0.308338
$832$	3.29211e6	0.164879
$833$	−2.91985e7	−1.45797
$834$	2.24042e6	0.111536
$835$	−1.48644e7	−0.737787
$836$	3.62799e6	0.179535
$837$	2.97338e6	0.146702
$838$	−2.33183e7	−1.14706
$839$	−1.26353e7	−0.619697	−0.309849	−	0.950786i	$-0.600278\pi$
$839$	−1.26353e7	−0.619697	−0.309849	+	0.950786i	$0.600278\pi$
$840$	3.32150e6	0.162419
$841$	−1.67763e7	−0.817912
$842$	−9.89667e6	−0.481071
$843$	4.39715e6	0.213109
$844$	6.43904e6	0.311147
$845$	−6.86752e6	−0.330871
$846$	−1.07394e6	−0.0515886
$847$	−5.38536e7	−2.57933
$848$	−4.61288e6	−0.220284
$849$	1.23461e7	0.587844
$850$	2.00556e6	0.0952112
$851$	2.26005e7	1.06978
$852$	−310937.	−0.0146748
$853$	2.23003e7	1.04939	0.524697	−	0.851289i	$-0.324179\pi$
$853$	2.23003e7	1.04939	0.524697	+	0.851289i	$0.324179\pi$
$854$	1.37011e6	0.0642851
$855$	−731025.	−0.0341993
$856$	−1.21034e7	−0.564577
$857$	−2.36161e7	−1.09839	−0.549195	−	0.835694i	$-0.685066\pi$
$857$	−2.36161e7	−1.09839	−0.549195	+	0.835694i	$0.685066\pi$
$858$	1.81742e7	0.842824
$859$	2.23718e7	1.03447	0.517235	−	0.855843i	$-0.326961\pi$
$859$	2.23718e7	1.03447	0.517235	+	0.855843i	$0.326961\pi$
$860$	3.22974e6	0.148909
$861$	−2.40102e7	−1.10380
$862$	−1.87882e7	−0.861225
$863$	2.88750e7	1.31976	0.659880	−	0.751371i	$-0.270607\pi$
$863$	2.88750e7	1.31976	0.659880	+	0.751371i	$0.270607\pi$
$864$	746496.	0.0340207
$865$	−1.09496e7	−0.497574
$866$	−1.70672e7	−0.773336
$867$	6.98665e6	0.315661
$868$	1.50527e7	0.678134
$869$	−6.24801e6	−0.280668
$870$	1.73932e6	0.0779077
$871$	5.38940e7	2.40711
$872$	6.39746e6	0.284915
$873$	−8.70031e6	−0.386366
$874$	3.74497e6	0.165832
$875$	3.60406e6	0.159137
$876$	5.28187e6	0.232556
$877$	−3.37814e6	−0.148313	−0.0741564	−	0.997247i	$-0.523626\pi$
$877$	−3.37814e6	−0.148313	−0.0741564	+	0.997247i	$0.523626\pi$
$878$	1.97162e7	0.863153
$879$	−1.89638e7	−0.827853
$880$	−4.01993e6	−0.174989
$881$	3.69886e7	1.60557	0.802783	−	0.596271i	$-0.203352\pi$
$881$	3.69886e7	1.60557	0.802783	+	0.596271i	$0.203352\pi$
$882$	−1.17926e7	−0.510434
$883$	2.20536e7	0.951871	0.475936	−	0.879480i	$-0.342110\pi$
$883$	2.20536e7	0.951871	0.475936	+	0.879480i	$0.342110\pi$
$884$	−1.03164e7	−0.444016
$885$	2.95101e6	0.126652
$886$	−7.69783e6	−0.329446
$887$	−1.40761e6	−0.0600723	−0.0300362	−	0.999549i	$-0.509562\pi$
$887$	−1.40761e6	−0.0600723	−0.0300362	+	0.999549i	$0.509562\pi$
$888$	−5.01948e6	−0.213612
$889$	−2.43121e7	−1.03174
$890$	1.31842e7	0.557930
$891$	4.12106e6	0.173906
$892$	7.09797e6	0.298691
$893$	1.19658e6	0.0502127
$894$	1.02028e7	0.426949
$895$	−9.08261e6	−0.379012
$896$	3.77913e6	0.157261
$897$	1.87602e7	0.778496
$898$	−1.18435e7	−0.490104
$899$	7.88240e6	0.325281
$900$	810000.	0.0333333
$901$	1.44553e7	0.593220
$902$	2.90590e7	1.18923
$903$	−1.67619e7	−0.684075
$904$	−1.08597e7	−0.441973
$905$	−1.42593e7	−0.578730
$906$	1.53623e6	0.0621780
$907$	1.51378e7	0.611003	0.305502	−	0.952192i	$-0.401176\pi$
$907$	1.51378e7	0.611003	0.305502	+	0.952192i	$0.401176\pi$
$908$	3.70091e6	0.148968
$909$	−1.29235e7	−0.518766
$910$	−1.85390e7	−0.742135
$911$	2.35678e7	0.940854	0.470427	−	0.882439i	$-0.344100\pi$
$911$	2.35678e7	0.940854	0.470427	+	0.882439i	$0.344100\pi$
$912$	−831744.	−0.0331133
$913$	−2.50323e7	−0.993858
$914$	−2.58272e7	−1.02261
$915$	334122.	0.0131933
$916$	−1.72212e7	−0.678146
$917$	−1.66807e7	−0.655074
$918$	−2.33928e6	−0.0916170
$919$	1.89047e7	0.738381	0.369191	−	0.929354i	$-0.379635\pi$
$919$	1.89047e7	0.738381	0.369191	+	0.929354i	$0.379635\pi$
$920$	−4.14955e6	−0.161633
$921$	1.20564e7	0.468349
$922$	−2.67988e7	−1.03822
$923$	1.73550e6	0.0670533
$924$	2.08628e7	0.803884
$925$	−5.44649e6	−0.209297
$926$	3.11437e7	1.19356
$927$	−1.64936e7	−0.630398
$928$	1.97895e6	0.0754338
$929$	2.38295e7	0.905891	0.452945	−	0.891538i	$-0.350373\pi$
$929$	2.38295e7	0.905891	0.452945	+	0.891538i	$0.350373\pi$
$930$	3.67084e6	0.139174
$931$	1.31393e7	0.496820
$932$	9.71863e6	0.366493
$933$	−1.12566e7	−0.423355
$934$	−72758.4	−0.00272908
$935$	1.25972e7	0.471243
$936$	−4.16657e6	−0.155450
$937$	−3.60203e7	−1.34029	−0.670144	−	0.742231i	$-0.733768\pi$
$937$	−3.60203e7	−1.34029	−0.670144	+	0.742231i	$0.733768\pi$
$938$	6.18670e7	2.29589
$939$	−2.81606e7	−1.04227
$940$	−1.32585e6	−0.0489412
$941$	−4.12047e7	−1.51696	−0.758478	−	0.651698i	$-0.774057\pi$
$941$	−4.12047e7	−1.51696	−0.758478	+	0.651698i	$0.774057\pi$
$942$	−6.65454e6	−0.244338
$943$	2.99960e7	1.09846
$944$	3.35759e6	0.122630
$945$	−4.20378e6	−0.153130
$946$	2.02865e7	0.737019
$947$	1.69181e7	0.613022	0.306511	−	0.951867i	$-0.400838\pi$
$947$	1.69181e7	0.613022	0.306511	+	0.951867i	$0.400838\pi$
$948$	1.43241e6	0.0517661
$949$	−2.94808e7	−1.06261
$950$	−902500.	−0.0324443
$951$	1.70371e7	0.610863
$952$	−1.18426e7	−0.423502
$953$	4.05573e7	1.44656	0.723281	−	0.690554i	$-0.242633\pi$
$953$	4.05573e7	1.44656	0.723281	+	0.690554i	$0.242633\pi$
$954$	5.83818e6	0.207686
$955$	1.76495e7	0.626216
$956$	1.45829e7	0.516060
$957$	1.09249e7	0.385600
$958$	−2.78921e7	−0.981899
$959$	−1.45140e7	−0.509614
$960$	921600.	0.0322749
$961$	−1.19933e7	−0.418919
$962$	2.80163e7	0.976052
$963$	1.53184e7	0.532289
$964$	−2.18158e7	−0.756097
$965$	7.38191e6	0.255182
$966$	2.15355e7	0.742528
$967$	−2.87676e7	−0.989322	−0.494661	−	0.869086i	$-0.664708\pi$
$967$	−2.87676e7	−0.989322	−0.494661	+	0.869086i	$0.664708\pi$
$968$	−1.49425e7	−0.512547
$969$	2.60642e6	0.0891735
$970$	−1.07411e7	−0.366539
$971$	5.29744e7	1.80309	0.901547	−	0.432681i	$-0.142432\pi$
$971$	5.29744e7	1.80309	0.901547	+	0.432681i	$0.142432\pi$
$972$	−944784.	−0.0320750
$973$	−1.43549e7	−0.486090
$974$	2.21154e7	0.746961
$975$	−4.52102e6	−0.152309
$976$	380157.	0.0127743
$977$	5.89342e7	1.97529	0.987646	−	0.156704i	$-0.0500869\pi$
$977$	5.89342e7	1.97529	0.987646	+	0.156704i	$0.0500869\pi$
$978$	−1.55185e6	−0.0518802
$979$	8.28119e7	2.76144
$980$	−1.45588e7	−0.484240
$981$	−8.09678e6	−0.268621
$982$	3.26301e7	1.07979
$983$	−6.01405e6	−0.198511	−0.0992553	−	0.995062i	$-0.531646\pi$
$983$	−6.01405e6	−0.198511	−0.0992553	+	0.995062i	$0.531646\pi$
$984$	−6.66200e6	−0.219339
$985$	1.90840e7	0.626728
$986$	−6.20142e6	−0.203142
$987$	6.88096e6	0.224831
$988$	4.64239e6	0.151304
$989$	2.09406e7	0.680766
$990$	5.08772e6	0.164982
$991$	−2.78350e7	−0.900342	−0.450171	−	0.892942i	$-0.648637\pi$
$991$	−2.78350e7	−0.900342	−0.450171	+	0.892942i	$0.648637\pi$
$992$	4.17660e6	0.134755
$993$	1.12881e7	0.363285
$994$	1.99224e6	0.0639552
$995$	−352233.	−0.0112790
$996$	5.73886e6	0.183306
$997$	−6.71600e6	−0.213980	−0.106990	−	0.994260i	$-0.534121\pi$
$997$	−6.71600e6	−0.213980	−0.106990	+	0.994260i	$0.534121\pi$
$998$	−3.56700e7	−1.13364
$999$	6.35278e6	0.201396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.h.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.h.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -230.660 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -230.660 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +628.114 q^{11} -144.000 q^{12} +803.737 q^{13} +922.640 q^{14} +225.000 q^{15} +256.000 q^{16} -802.223 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +2075.94 q^{21} -2512.46 q^{22} -2593.47 q^{23} +576.000 q^{24} +625.000 q^{25} -3214.95 q^{26} -729.000 q^{27} -3690.56 q^{28} -1932.57 q^{29} -900.000 q^{30} -4078.71 q^{31} -1024.00 q^{32} -5653.03 q^{33} +3208.89 q^{34} +5766.50 q^{35} +1296.00 q^{36} -8714.38 q^{37} -1444.00 q^{38} -7233.64 q^{39} +1600.00 q^{40} -11566.0 q^{41} -8303.76 q^{42} -8074.36 q^{43} +10049.8 q^{44} -2025.00 q^{45} +10373.9 q^{46} +3314.63 q^{47} -2304.00 q^{48} +36397.0 q^{49} -2500.00 q^{50} +7220.01 q^{51} +12859.8 q^{52} -18019.1 q^{53} +2916.00 q^{54} -15702.8 q^{55} +14762.2 q^{56} -3249.00 q^{57} +7730.29 q^{58} +13115.6 q^{59} +3600.00 q^{60} +1484.99 q^{61} +16314.8 q^{62} -18683.5 q^{63} +4096.00 q^{64} -20093.4 q^{65} +22612.1 q^{66} +67054.3 q^{67} -12835.6 q^{68} +23341.2 q^{69} -23066.0 q^{70} +2159.28 q^{71} -5184.00 q^{72} -36679.7 q^{73} +34857.5 q^{74} -5625.00 q^{75} +5776.00 q^{76} -144881. q^{77} +28934.5 q^{78} -9947.26 q^{79} -6400.00 q^{80} +6561.00 q^{81} +46263.9 q^{82} -39853.2 q^{83} +33215.0 q^{84} +20055.6 q^{85} +32297.4 q^{86} +17393.2 q^{87} -40199.3 q^{88} +131842. q^{89} +8100.00 q^{90} -185390. q^{91} -41495.5 q^{92} +36708.4 q^{93} -13258.5 q^{94} -9025.00 q^{95} +9216.00 q^{96} -107411. q^{97} -145588. q^{98} +50877.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * q^99

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